Existence of solutions for a class of third-order two-point boundary value problems
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国家科技期刊平台
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考察了三阶非线性常微分方程边值问题{u'''(t)= f(t,u(t),u'(t),u''(t)),a.e.0<t<1,u(0)= u'(0)= u'(1)= 0,其中f:[0,1]×R3→R 满足Carathéodory条件.在非线性项 f 满足适当增长性条件下,三阶非线性常微分方程边值问题至少存在1个解.基于Leray-Schauder不动点定理证明了主要结果.
In this paper,we consider the boundary value problems of third-order nonlinear ordinary differential equation{u'''(t)= f(t,u(t),u'(t),u''(t)),a.e.0<t<1,u(0)= u'(0)= u'(1)=0,where f:[0,1]×R3→R satisfies Carathéodory conditions.Under some suitable growth conditions on f,we show that the above problem has at least one solution.The proof of the main results is based on Leray-Schauder fixed point theorem.
third-order ordinary differential equationboundary value problemLeray-Schauder fixed point theoremexistence
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